IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v175y2023ip2s0960077923008470.html
   My bibliography  Save this article

The exact solutions of the variable-order fractional stochastic Ginzburg–Landau equation along with analysis of bifurcation and chaotic behaviors

Author

Listed:
  • Qi, Jianming
  • Li, Xinwei
  • Bai, Leiqiang
  • Sun, Yiqun

Abstract

This article explores the exact solutions of the variable order fractional derivative of the stochastic Ginzburg–Landau equation (GLE) using the G′G2-expansion method with the assistance of Matlab R2021a software. The paper presents three key aspects that contribute to its novelty: (1) Our study introduces and examines the variable order fractional derivative of the stochastic Ginzburg–Landau equation (VOFDSGLE) for the first time, demonstrating our best cognitive effort. We successfully obtain a significant number of exact solutions and provide illustrative examples and visual representations of the VOFDSGLE. These obtained solutions have the potential to offer enhanced availability and practicality in understanding the mechanisms behind the complex physical phenomena observed in various fields. (2) Additionally, we investigate the phase portraits of the variable-order fractional stochastic Ginzburg–Landau equation under a specific condition. We analyze the associated sensitivity and chaotic behaviors, which have not been examined in prior studies on stochastic Ginzburg–Landau equation (Mohammed et al., 2021; Alhojilan and Ahmed, 2023). This exploration adds a unique contribution to the existing literature and offers valuable insights into the dynamics of the system. (3) Our numerical observations underscore the significant impact of multiplicative noise on the solutions. The progressive degradation of patterns and the tendency towards planar surfaces indicate the disruption caused by increasing noise intensity. Moreover, the convergence of solution magnitudes to zero underlines the stabilizing influence of the multiplicative noise. Furthermore, we advance the existing knowledge regarding the response of the stochastic GLE model to small noise, offering valuable insights into the system’s transition behaviors in the energy landscape.

Suggested Citation

  • Qi, Jianming & Li, Xinwei & Bai, Leiqiang & Sun, Yiqun, 2023. "The exact solutions of the variable-order fractional stochastic Ginzburg–Landau equation along with analysis of bifurcation and chaotic behaviors," Chaos, Solitons & Fractals, Elsevier, vol. 175(P2).
    • Handle: RePEc:eee:chsofr:v:175:y:2023:i:p2:s0960077923008470
    DOI: 10.1016/j.chaos.2023.113946
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077923008470
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2023.113946?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Nguyen Tien, Dung, 2013. "A stochastic Ginzburg–Landau equation with impulsive effects," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(9), pages 1962-1971.
    2. Alquran, Marwan & Yousef, Feras & Alquran, Farah & Sulaiman, Tukur A. & Yusuf, Abdullahi, 2021. "Dual-wave solutions for the quadratic–cubic conformable-Caputo time-fractional Klein–Fock–Gordon equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 185(C), pages 62-76.
    3. Shao-Wen Yao & Esin Ilhan & P. Veeresha & Haci Mehmet Baskonus, 2021. "A Powerful Iterative Approach For Quintic Complex Ginzburg–Landau Equation Within The Frame Of Fractional Operator," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(05), pages 1-13, August.
    4. Hong Lu & Linlin Wang & Mingji Zhang, 2022. "Dynamics of Fractional Stochastic Ginzburg–Landau Equation Driven by Nonlinear Noise," Mathematics, MDPI, vol. 10(23), pages 1-36, November.
    5. Muhammad Arshad & Aly R. Seadawy & Dianchen Lu, 2017. "Bright–dark solitary wave solutions of generalized higher-order nonlinear Schrödinger equation and its applications in optics," Journal of Electromagnetic Waves and Applications, Taylor & Francis Journals, vol. 31(16), pages 1711-1721, November.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Çelik, Nisa & Tetik, Duygu, 2024. "New dynamical analysis of the exact traveling wave solutions to a (3+1)-dimensional Gardner-KP equation by three efficient architecture," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Asjad, Muhammad Imran & Sunthrayuth, Pongsakorn & Ikram, Muhammad Danish & Muhammad, Taseer & Alshomrani, Ali Saleh, 2022. "Analysis of non-singular fractional bioconvection and thermal memory with generalized Mittag-Leffler kernel," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    2. Khirsariya, Sagar R. & Chauhan, Jignesh P. & Rao, Snehal B., 2024. "A robust computational analysis of residual power series involving general transform to solve fractional differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 216(C), pages 168-186.
    3. Kumar, Raj & Kumar, Avneesh, 2022. "Dynamical behavior of similarity solutions of CKOEs with conservation law," Applied Mathematics and Computation, Elsevier, vol. 422(C).
    4. Guirao, Juan Luis García & Alsulami, Mansoor & Baskonus, Haci Mehmet & Ilhan, Esin & Veeresha, P., 2023. "Analysis of nonlinear compartmental model using a reliable method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 214(C), pages 133-151.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:175:y:2023:i:p2:s0960077923008470. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.